Summary of Grade 8 Maths Term 4 Lesson 17 Relative Frequency

Summary of Key Concepts and Lessons on Relative Frequency

• Definition of Relative Frequency vs. Probability:
  • Probability: Theoretical calculation of the likelihood of an event occurring.
  • Relative Frequency: Calculated using actual results from experiments or Trials. It is the ratio of successful outcomes to the total number of Trials.
• Calculating Relative Frequency:
  • Formula:

    Relative Frequency = Number of Successful Outcomes / Total Number of Trials

  • Example with a coin flip:
    • If you flip a coin 20 times and get heads 9 times, the Relative Frequency of heads is 9/20.
• Practical Examples:
  • Coin Flipping:
    • After 5 Trials: 1 head → Relative Frequency = 1/5
    • After 10 Trials: 4 heads → Relative Frequency = 4/10 = 2/5
    • After 20 Trials: 9 heads → Relative Frequency = 9/20
  • Dice Rolling:
    • Rolling a die 30 times to find the frequency of rolling a six.
• Using Probability for Predictions:
  • To estimate expected outcomes, multiply the Probability of an event by the total number of Trials.
  • Example: If the Probability of landing on a number between 2 and 7 on a Spinner is 4/10 and you plan to conduct 100 Trials, you would expect approximately 40 occurrences.
• Activity Example:
  • Drawing Marbles from a bag and calculating expected outcomes based on the Probability of drawing different colored Marbles.
• Comparison of Relative Frequency and Probability:
  • Conducting more Trials generally leads to relative frequencies that are closer to the theoretical probabilities.
  • Example: After 10 Trials, the Relative Frequency of drawing a heart was 10%, while after 50 Trials, it was 26%, compared to a theoretical Probability of 25%.
• Conclusion:

  The lesson emphasizes the importance of practice in mastering the concepts of Relative Frequency and Probability.

Methodology for Calculating Relative Frequency

• Identify the successful outcomes from your Trials.
• Count the total number of Trials conducted.
• Use the formula to calculate Relative Frequency.
• For predictions, calculate the Probability first and then multiply by the number of Trials.

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